How do I select all vertices in edit mode?
press A twice



If you want a simple horn shape you can use the Data>Geometry>Bevel slider in the Properties of the BezierCurve to give you curve depth. Be sure to set the Shape>Fill to Full, increase the Geometry>Bevel above 0 to give it depth, and increase the Geometry>Resolution to make it more rounded:


You can then press Alt+S to scale the diameter at the vertices. 

You could even use a non circular Mesh BezierCurve as Bevel Object, and twist the vertices with Ctrl+T to get a cartoony twisted horn look.